For each set of values, determine which is greater without using a calculator. √19 + √3 or √5 +√13

The factors for given equation are -2/3 and -2.

Rewriting the equation firstly -

3x² + 8x + 4 = 0

ax² + bx + c = 0

Factorizing the equation as per mentioned two rules -

6 and 2 are the suitable factors for given expression -

3x² + 6x + 2x + 4 = 0

3x (x + 2) + 2(x + 2) = 0

(3x + 2) (x + 2) = 0

3x + 2 = 0

3x = -2

x = -2/3

x + 2 = 0

x = -2

So, the two factors of equation are -2/3 and -2.

To check the factors, we will keep the value of x in equation -

When x = -2/3

3x² + 8x + 4 = 0

3(-2/3)² + 8(-2/3) + 4 = 0

3(4/9) - 16/3 + 4 = 0

4/3 - 16/3 + 4 = 0

Multiplying the equation with 3/4

1 - 4 + 3 = 0

- 3 + 3 = 0

0 = 0

When x = -2

3x² + 8x + 4 = 0

3(-2)² + 8(-2) + 4 = 0

12 - 16 + 4 = 0

- 4 + 4 = 0

0 = 0

Since for both values of x, Left hand Side and Right Hand Side of equation is same, the two resultant factors are correct.

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Answer:

The frog will catch the fly after 2 seconds of his jump.

Step-by-step explanation:

It is given that a frog is about to hop from the bank of a creek. The path of the jump can be modeled by the equation h(x) = -x² + 4x + 1, where h(x) is the frog's height above the water and x is the number of seconds since the frog jumped and a fly is cruising at a height of 5 feet above the water.

Now, let us assume that the frog catches the fly that is cruising at a height of 5 feet above the water;

=> h = 5 feet

So, let us put the value of h = 5 for time x;

=> h(x) = -x² + 4x + 1

=> 5 = -x² + 4x + 1

=> x² - 4x - 1 + 5 = 0

=> x² - 4x + 4 = 0

Now, on solving the above equation we get;

=> x² - 4x + 4 = 0

=> x² - (2 + 2)x + 4 = 0

=> x² - 2x - 2x + 4 = 0

=> x (x - 2) - 2 (x - 2) = 0

=> (x - 2) (x - 2) = 0

On comparing and solving for the value of x we get;

=> (x - 2) = 0

=> x = 2

and

=> (x - 2) = 0

=> x = 2

Therefore, the frog will catch the fly after 2 seconds of his jump.

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Answer:

Area: 6[tex]x^{2}[/tex] - 8x

Perimeter: 10x - 8

Step-by-step explanation:

Area:

Multiple the 2 sides together

2x(3x -4)  Distribute the 2x

2x(3x)- 2x(4)

6[tex]x^{2}[/tex] -8x

Perimeter:

Add the four sides together

3x -4 + 3x -4 +2x + 2x  Combine like terms

10x - 8

The solution of the equation 3√2 x + 6 = 18 is 2√2.

An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal.

Consider the equation,

3√2 x + 6 = 18

Subtracting 6 from each side of the equation.

3√2 x + 6 - 6 = 18 - 6

3√2 x = 12

Dividing each side of the equation by 3.

( 3√2 x / 3 ) = ( 12/3 )

√2 x = 4

Dividing each side of the equation by √2.

( √2x/√2 ) = ( 4/√2 )

x = 2√2

Now checking the extraneous solution:

x = 2√2

[tex]3\sqrt{2}x + 6 = 18\\ 3\sqrt{2} \times 2\sqrt{2} + 6 = 18\\ 6(2) + 6 = 18\\ 18 = 18[/tex]

The solution for the equation is 2√2.

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Answer:

-10

Step-by-step explanation:

[tex]2\left(-5\right)\left(-1\right)\left(-1\right)\\(-5)(-1) = |5|\\= 2 \times 5\left(-1\right)\\2 \times 5 = 10\\10 \times |-1| = -10\\= -10[/tex]

Answer:

-10

Step-by-step explanation:

Let's solve the problem,

→ 2(-5)(-1)(-1)

→ (2 × -5) × (-1 × -1)

→ -10 × 1 = -10

Thus, the answer is -10.

Answer: 1. 0.937

2. 20.786

3. 35.001

Step-by-step explanation:

1. 0.9+0.03+0.007=

0.900+0.030+0.007=0.937

2. 20 +0.7 + 0.08 + 0.006=

20.000 +0.700 + 0.080 + 0.006=20.786

3. 35 + 0.01 - 0.009=

35.000 + 0.010 - 0.009=

35.010 - 0.009=35.001

Answer:

21 hours

Step-by-step explanation:

If he worked 2/3 at home you need to divide 31.5 by 3 = 10.5

Then multiply by 2 = 21

Hope this helps! Have a great day :)

Answer:

B

Step-by-step explanation:

calculate the distance between A and B using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (1, 6 ) and (x₂, y₂ ) = B (x, - 2 )

d = [tex]\sqrt{(x-1)^2+(-2-6)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+(-8)^2}[/tex]

   = [tex]\sqrt{(x-1)^2+64}[/tex]

given AB = 10, then equating gives

[tex]\sqrt{(x-1)^2+64}[/tex] = 10 ( square both sides to clear the radical )

(x - 1)² + 64 = 10² = 100 ( subtract 64 from both sides )

(x - 1)² = 36 ← take square root of both sides

x - 1 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 1 to both sides )

x = 1 ± 6

then

x = 1 - 6 = - 5

x = 1 + 6 = 7

from the list then x = - 5 is a possible value

Answer:

-10 and -10

Step-by-step explanation:

Can you use the same number twice?

Based on theword problem, the inequality of the word problem is 7/2 + 4h >=  1

Inequalities are used to represent expressions that do not have equal values i.e. unequal expression

The word problem is given as

Half of 7 added to product of h and 4 is at least 1

At least 1 means greater than or equal to 1

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to product of h and 4 >=  1

The product of h and 4 means 4h

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ Half of 7 added to 4h >=  1

Half of 7 means 7/2

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 added to 4h >=  1

added to means +

So, the word problem becomes

Half of 7 added to product of h and 4 is at least 1 ⇒ 7/2 + 4h >=  1

Hence, the inequality of the word problem is 7/2 + 4h >=  1

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The value of x in the triangle is 100 units.

A right triangle is a triangle that has one of its angles as 90 degrees.

The triangles formed are similar, therefore, they form a ratio or proportion.

Therefore, using similarity principle of triangles,

36 / 60 = 60 / x

cross multiply

36x = 60 × 60

36x = 3600

divide both sides by 36

36x = 3600

36x / 36 = 3600 / 36

x = 100

Therefore, the value of x in the triangle is 100 units.

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Answer:

Two shapes are congruent if their corresponding sides and corresponding angles are congruent.

Step-by-step explanation:

This is the definition of congruency.

The required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given the trigonometry identity;

d=94 secθ.

If the object is sighted at an angle of  25°, then;

d=94 sec25

d = 94 × 1/cos25

d = 94 × 1.1033

d = 103.71feet

If the object is sighted at an angle of  55°, then;

d=94 sec55

d = 94 × 1/cos55

d = 94 × 1.7434

d = 163.88feet

Hence the required distance of object far from 25° and 55° are 103.71feet and 163.88feet respectively.

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Step-by-step explanation:

the first suspicion we get from the first terms is that the creation algorithm is a multiplication by 3.

-1/3 × 3 = -1

-1 × 3 = -3

-3 × 3 = -9

then the next term would be

-9 × 3 = -27

and the next

-27 × 3 = -81

and the 7th term, that we have already defined, would be

-81 × 3 = -243

we are correct !

so, the missing terms are

-27, -81

_what is this this is futo balis subina to amake dis_

Answer:

C. 40 times greater is the distance of Pluto from the Sun than the distance of Venus from the sun.

Answer: (1/14, 10/7, -13/14)

Step-by-step explanation:

3x+2y−z=82x+2z=−4x+3y=4 ==> convert this to system of equations

3x+2y−z=4

82x+2z=4

−4x+3y=4

(3x+2y−z=4)*2

6x+4y−2z=8 ==> add this equation

82x+2z=4 ==> add this equation

88x+4y=12 ==> add the top 2 equations

(−4x+3y=4)*4

-16x+12y=16

(88x+4y=12)*3   ==> multiply by 3 to get 12y

264x+12y=36

-16x+12y=16

264x-(-16x)=36-16

264x+16x=20

280x=20

280x/280=20/280

x=1/14

−4x+3y=4

−4(1/14)+3y=4

-4/14 + 3y=4

-2/7 + 3y=4

(-2/7 + 3y=4)*7 ==> multiply equation by 7 to remove fractions

-2+21y=28

21y=30

y=30/21

y=10/7

3x+2y−z=4

3(1/14)+2(10/7)−z=4

3/14 + 20/7 - z=4

(3/14 + 20/7 - z=4)*14 ==> multiply equation by 14 to remove fractions

3 + 20*14/7 - 14z=56

3 + 280/7 - 14z=56

3+40-14z=56

43-14z=56

43-43-14z=56-43

-14z=13

z=-13/14

Answer: (1/14, 10/7, -13/14)

x = 13/2 is not an extraneous solution.

[tex](2x+3)^{3/4}[/tex] - 3 = 5

Adding 3 on both the sides of the equation, we get

[tex](2x+3)^{3/4}[/tex] - 3 + 3= 5 + 3

[tex](2x+3)^{3/4}[/tex] = 8

On the right hand side of the equation, 8 can also be written as

[tex](2x+3)^{3/4} = 2^{(3/4)*4}[/tex]

Taking power 4/3 on both the side of the equation, we get

(2x + 3) = 2⁴

2x + 3 = 16

2x = 13

x = 13/2

Check for extraneous solution and putting x = 13/2 in the original equation, we get

[tex](2(13/2) + 3)^{3/4}[/tex] - 3 = 5

[tex]16^{3/4}[/tex] - 3 = 5

8 - 3 = 5

5 = 5

⇒ LHS = RHS

∴   x = 13/2 is not an extraneous solution.

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Based on the amount that Nick is left with at the end of the month, the amount he earns is $2,400

The amount of $300 that is left is 25% of 50% of Nick's income as the other 75% of the 50% went to paying for the car and other expenses.

25% of 50% is:

= 25% x 50%

= 12.5%

The amount Nick makes per month is:

= Amount remaining / Amount remaining in percentage terms

= 300 / 12.5%
= $2,400

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Answer:

m + n + p = a

Step-by-step explanation:

m - a = n- p

M = a - n - p

M + n = a - p

M + n + p = a

Charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

The first step is to convert miles per hour to feet per second.

(69.6 mi/hr)* (5280 feet/mi)*(1 hr/3600 sec) = 102.08 feet/sec

We know that,

Speed = [tex]\frac{Distance}{Time}[/tex]

Here, we have given,

Time = 4.06 s

Speed (feet/sec) = 102.08 feet/sec

We need to find, the distance charlotte traveled in feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

Putting the values in the formula, we get

Distance = Speed x Time

= 102.08 x 4.06

= 414.44 Feet

Hence, charlotte traveled in 414.44 feet during the time when she looks down at her phone and takes her eyes off the road for 4.06 s.

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Answer:

that is definitaly 18

Step-by-step explanation:

i will break it down 3+3+3=9    3+3+3=9 again  9+9=18

[tex]answer[/tex]

18

Break it down: 3+3+3= 9, Another 3+3+3= 9 (3 addition in 6 places will give 18). 9+9 = 18

Answer: that’s easily C because look down

Step-by-step explanation:

calculator lol I saw it don’t worry niu

the answer is the 0,1 because the lines all have different slopes but always start at 1.

the inequality to determine if a child's height satisfies the regulation is:

30in < h < 50 in.

Here we know that the allowed height of the child can be any value between 30 inches and 50 inches (not included, so we need to use the symbols > and <)

So, if we define h as the height, then h must be larger than 30 inches, so we can wrte:

h > 30 in

And h must be smaller than 50 inches, then:

h < 50 in.

If we write these two inequalities as one, we get:

30in < h < 50 in.

That is the inequality to determine if a child's height satisfies the regulation.

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The line of the graph is a solid line and the region to be shaded depends on the type of the inequality

The graph represents the given parameter

On the graph, we have a straight continuous line

A straight continuous line is an illustration of a solid line

This means that the line of the graph is a solid line

Hence, the line of the graph is a solid line

The graph represents the given parameter

On the graph, we can see that no region of the graph is shaded

This means that the shaded region would be determined by the type of the inequality

≥ means that the region would be shaded above

≤ means that the region would be shaded below

Hence, the region to be shaded depends on the type of the inequality

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Given that  ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.

Supplementary angles are angles that sum up to 180 degrees.

Given the data in the question;

Since ∠ABC and ∠DEF are supplementary, it means they sum up to 180 degrees.

Measure of ∠ABC + Measure of ∠DEF = 180°

Plug in the given values and solve for x

(6x + 8) + (12x − 8) = 180

6x + 8 + 12x − 8 = 180

6x + 12x + 8 - 8 = 180

18x + 0 = 180

18x = 180

x = 180/18

x = 10

Now, the numerical measure of each angle will be;

Measure of ∠ABC = (6x + 8)° = 6(10) + 8 = 60 + 8 = 68°

Measure of ∠DEF = (12x − 8)° = 12(10) - 8 = 120 - 8 = 112°

Given that  ∠ABC and ∠DEF are supplementary, the numerical value of ∠ABC and ∠DEF are 68° and 112° respectively.

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The equation of the function given as (x)= 5 * 2^x is an exponential function

The equation of the function is given as

f(x)= 5 * 2^x

An exponential function is represented as

f(x) = a * b^x

Where

Initial value = a

Rate = b

This means that

a = 5

b = 2

Hence, the equation of the function given as (x)= 5 * 2^x is an exponential function

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answer: 8 wholes and 3/4

When the cool rock that is rolling down the side of the volcano is compared to the mass of hot lava that is slowly flowing, the rock has 2. less thermal energy and more mechanical energy.

The mechanical energy that an object has refers to the combination of kinetic and potential energy. The rock will have more mechanical energy than the hot lava as it is moving faster.

Thermal energy on the other hand refers to how much heat/ energy is in an object. The rock is cool as opposed to the hot lava which would have more thermal energy as a result of its heat.

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